Power means and the reverse Hölder inequality

Victor D. Didenko, and Anatolii A. Korenovskyi. "Power means and the reverse Hölder inequality." Studia Mathematica 207.1 (2011): 85-95. <http://eudml.org/doc/285529>.

@article{VictorD2011,
abstract = {Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means $_\{α\}w(x): = ((1/x) ∫_\{0\}^\{x\} w^\{α\}(t)dt)^\{1/α\}$, x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.},
author = {Victor D. Didenko, Anatolii A. Korenovskyi},
journal = {Studia Mathematica},
keywords = {power means; reverse Hölder inequality; self-improvement property},
language = {eng},
number = {1},
pages = {85-95},
title = {Power means and the reverse Hölder inequality},
url = {http://eudml.org/doc/285529},
volume = {207},
year = {2011},
}

TY - JOUR
AU - Victor D. Didenko
AU - Anatolii A. Korenovskyi
TI - Power means and the reverse Hölder inequality
JO - Studia Mathematica
PY - 2011
VL - 207
IS - 1
SP - 85
EP - 95
AB - Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means $_{α}w(x): = ((1/x) ∫_{0}^{x} w^{α}(t)dt)^{1/α}$, x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.
LA - eng
KW - power means; reverse Hölder inequality; self-improvement property
UR - http://eudml.org/doc/285529
ER -